A small strand of recent literature is occupied with identifying simultaneity in multiple equation systems through autoregressive conditional heteroscedasticity. Since this approach assumes that the structural innovations are uncorrelated, any contemporaneous connection of the endogenous variables needs to be exclusively explained by mutual spillover effects. In contrast, this paper allows for instantaneous covariances, which become identifiable by imposing the constraint of structural constant conditional correlation (SCCC). In this, common driving forces can be modelled in addition to simultaneous transmission effects. The new methodology is applied to the Dow Jones and Nasdaq Composite indexes in a small empirical example, illuminating scope and functioning of the SCCC model.